Calculating Free Energy Contributions

Similarly, we often try to interpret changes in the free energy in terms of contributions to the potential energy function. For instance, one might want to know whether AA is primarily driven by electrostatic or van der Waals interactions. Alternatively, one might be interested in finding out what are the contributions to AA arising from 

Addressing these issues from an FEP perspective is the main goal of this section. The main conclusions that we reach are, however, of a general nature and are independent of the method used for calculating the free energy. 

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In Section III we described an approximation to the nonpolar free energy contribution based on the concept of the solvent-accessible surface area (SASA) [see Eq. (15)]. In the SASA/PB implicit solvent model, the nonpolar free energy contribution is complemented by a macroscopic continuum electrostatic calculation based on the PB equation, thus yielding an approximation to the total free energy, AVP = A different implicit... 

FEP calculations for paths A, B and C were performed with a 40 ps equilibration run prior to the sampling for all points along the path. The free energy contributions were sampled for 20 ps for each point on the MEP. In all cases a time step of 2.0 fs was employed, maintaining a constant temperature of 300 K. The SHAKE [47] algorithm was used to constrain all bonds involving hydrogen atoms. 

The thermodynamic chemical potential is then obtained by averaging the Boltzmann factor of this conditional result using the isolated solute distribution function Sa Sn). Notice that the fluctuation contribution necessarily lowers the calculated free energy. 

A solvated MD simulation is performed to determine an ensemble of conformations for the molecule of interest. This ensemble is then used to calculate the terms in this equation. Vm is the standard molecular mechanics energy for each member of the ensemble (calculated after removing the solvent water). G PB is the solvation free energy calculated by numerical integration of the Poisson-Boltzmann equation plus a simple surface energy term to estimate the nonpolar free energy contribution. T is the absolute temperature. S mm is the entropy, which is estimated using... 

We also adopt the above combination rule (Eq. [6]) for the general case of exp-6 mixtures that include polar species. Moreover, in this case, we calculate the polar free energy contribution Afj using the effective hard sphere diameter creff of the variational theory. 

Item (2) contributes to the calculated free energy of formation of the product from a system coming from the intersection. 

Since COSMO-RS allows for a rather fundamental calculation of the chemical potential of molecules in various chemical environments, there are many application areas that go beyond the calculation of activity and partition coefficients, which are directly accessible from the differences of chemical potentials in different phases. Often, such applications require the addition of some empiricism to the model because they involve free-energy contributions that are not directly accessible by COSMO-RS. Nevertheless, in many cases, the COSMO-RS is a robust starting point for such empirical extensions, and the resulting models are still less empirical and more fundamental than many other approaches. Without going into details we will describe some extended application areas in this chapter. 

Contact. This free energy contribution is calculated using the expression... 

Whereas the charging approach could be applied to any geometry but only at constant surface charge or potential, the Langmuir expression could be employed for any surface conditions but only for parallel planar plates. The addition of electrostatic, entropic, and chemical contributions would allow the calculation of the free energy of interaction for systems of any shape and any surface conditions, if one could derive a general expression for the chemical free energy contribution. 

M. Fornabaio, F. Spyrakis, A. Mozzar-elli, P. Cozzini, D. J. Abraham, G. E. Kellogg, Simple, intuitive calculations of free energy of binding for protein-ligand complexes. 3. The free energy contribution of structural water molecules in HIV-1 protease complexes,/. Med. 

The anharmonic free energy is evaluated for empty hydrate and cubic ice (ice Ic). The calculated free energy due to the anharmonic potential energy surface is given in Table 1. The anharmonic contribution to the free energy of empty... 

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